=== Test: test_D_measurement_plus_mlogit ===
Timestamp: 2025-12-10 09:51:49.483612

--- Gradient Check ---
Pass: TRUE
Max error: 1.11e-05

param_idx param_value fixed analytical finite_diff abs_error rel_error pass
1 1 TRUE -142.674499492856 -142.674560546875 6.10540190564279e-05 4.2792505421013e-07 TRUE
2 2 FALSE -16.7119549860307 -16.7119598388672 4.85283650064616e-06 2.90381053295728e-07 TRUE
3 0.5 FALSE 128.101731395634 128.101745605469 1.42098346600505e-05 1.10926159459328e-07 TRUE
4 1.5 FALSE 24.1434250994612 24.1433919270833 3.31723779076754e-05 1.37397338401584e-06 TRUE
5 1.2 FALSE -69.0580329864808 -69.0580622355143 2.92490334885542e-05 4.23542632702376e-07 TRUE
6 0.6 FALSE 60.6354596133227 60.6354827880859 2.31747632426504e-05 3.82198049344203e-07 TRUE
7 1 FALSE -61.6711937310878 -61.6712036132812 9.8821934173543e-06 1.60239995952116e-07 TRUE
8 0.8 FALSE -159.448690387837 -159.448654174805 3.62130322457688e-05 2.27114066488565e-07 TRUE
9 0.4 FALSE 212.427313383062 212.427291870117 2.15129450396034e-05 1.01272039247937e-07 TRUE
10 0.5 FALSE -27.0888852766863 -27.0888671875 1.80891862591182e-05 6.67771971928944e-07 TRUE
11 0.6 FALSE -3.36989669905156 -3.36993408203125 3.73829796886938e-05 1.10930892945422e-05 TRUE
12 0.7 FALSE 2.90561121503501 2.90559387207031 1.73429646981305e-05 5.96881927128141e-06 TRUE
13 1 FALSE 16.0498231783185 16.0498809814453 5.78031268148038e-05 3.60146762967451e-06 TRUE
14 -0.5 FALSE 6.18416241207914 6.18414306640625 1.93456728876384e-05 3.12827059139831e-06 TRUE
15 0.9 FALSE 9.1555221768743 9.155517578125 4.59874929781279e-06 5.02292662164774e-07 TRUE

--- Hessian Check ---
Pass: TRUE
Max error: 5.36e-05

Summary of relative errors:
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
0.00e+00 1.90e-08 8.40e-08 1.42e-04 4.67e-07 1.68e-02 

--- Estimation Comparison ---
Default init converged: TRUE
True init converged: TRUE
Default estimates reasonable: TRUE
True init estimates reasonable: TRUE

Parameter estimates:
parameter true_value default_init est_default se_default est_true_init se_true_init z_default z_true_init
f_var 1 1 0.934418097439613 0.0713040202945172 0.934418095146248 0.0713040201681866 -0.919750419254129 -0.919750453046861
T1_int 2 2.01960891905375 2.01694896011797 0.0411906706797389 2.01694896047974 0.0411906706726237 0.411475701615707 0.411475710469549
T1_sigma 0.5 1.06384096857368 0.475224232143668 0.0223395288644922 0.475224232243019 0.0223395288701103 -1.10905507482354 -1.10905507009731
T2_int 1.5 1.55094114192773 1.54778826327732 0.0492484847645311 1.54778826370461 0.0492484847701664 0.970349920526652 0.970349929091825
T2_lambda 1.2 0.5 1.18531102415246 0.0413253364708842 1.18531102472725 0.0413253365135963 -0.355447217178582 -0.355447202902086
T2_sigma 0.6 1.26928237763899 0.581595237811886 0.025849093554835 0.581595237774334 0.0258490935698261 -0.712008030342375 -0.712008031382207
T3_int 1 1.00263713524346 1.00056520563891 0.0326214565914478 1.00056520591967 0.0326214565948122 0.0173261925729583 0.0173262011777043
T3_lambda 0.8 0.5 0.778932928871614 0.02779719948307 0.778932929263733 0.027797199508559 -0.757884661770219 -0.757884646968861
T3_sigma 0.4 0.839109411254507 0.392957115138728 0.0176355836496964 0.392957115088957 0.0176355836555435 -0.399356494299704 -0.399356496989521
y1_int 0.5 -0.0378191154681297 0.211088086382568 0.167097795848302 0.21108808668001 0.167097795859509 -1.72899895028967 -1.72899894839366
y1_beta1 0.6 0.721571401567438 0.745320386502742 0.151576212865338 0.745320386506157 0.151576212865021 0.958728178753528 0.958728178778056
y1_loading 0.7 0.5 0.842367478380808 0.171585719273198 0.842367478682139 0.17158571935486 0.829716359752126 0.829716361113395
y2_int 1 0.831972783489226 1.04304119854071 0.145632622262384 1.04304119891399 0.145632622274672 0.295546408984959 0.29554641152319
y2_beta1 -0.5 -0.442889196251955 -0.410417790666849 0.134952560542707 -0.410417790631027 0.134952560542701 0.663805184376637 0.663805184642107
y2_loading 0.9 0.5 1.10163072933577 0.161357008170887 1.10163072987262 0.16135700825162 1.24959387646945 1.24959387917134

Likelihood comparison:
source loglik convergence
True parameters -2080.25288990059 NA
Est (default init) -2071.32267975607 0
Est (true init) -2071.32267975607 0

--- Overall Result ---
Test passed: TRUE
